The Schur and (weak) Dunford-Pettis properties in Banach lattices

Journal of the Australian Mathematical Society

Anna Kamińska¹ 

[1] Mieczysław Mastyło

关键词: primary 46B20;    46E30;    46B42;    46B45;   

DOI  :  10.1017/S144678870000882X

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We study the Schur and (weak) Dunford-Pettis properties in Banach lattices. We show that l1, c0 and l∞ are the only Banach symmetric sequence spaces with the weak Dunford-Pettis property. We also characterize a large class of Banach lattices without the (weak) Dunford-Pettis property. In MusielakOrlicz sequence spaces we give some necessary and sufficient conditions for the Schur property, extending the Yamamuro result. We also present a number of results on the Schur property in weighted Orlicz sequence spaces, and, in particular, we find a complete characterization of this property for weights belonging to class ∧. We also present examples of weighted Orlicz spaces with the Schur property which are not L1-spaces. Finally, as an application of the results in sequence spaces, we provide a description of the weak Dunford-Pettis and the positive Schur properties in Orlicz spaces over an infinite non-atomic measure space.

【 授权许可】

Unknown